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<li><a class="reference internal" href="#">Comparison of kernel ridge regression and SVR</a></li>
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<p class="first admonition-title">Note</p>
<p class="last">Click <a class="reference internal" href="#sphx-glr-download-auto-examples-plot-kernel-ridge-regression-py"><span class="std std-ref">here</span></a> to download the full example code</p>
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<div class="sphx-glr-example-title section" id="comparison-of-kernel-ridge-regression-and-svr">
<span id="sphx-glr-auto-examples-plot-kernel-ridge-regression-py"></span><h1>Comparison of kernel ridge regression and SVR<a class="headerlink" href="#comparison-of-kernel-ridge-regression-and-svr" title="Permalink to this headline">¶</a></h1>
<p>Both kernel ridge regression (KRR) and SVR learn a non-linear function by
employing the kernel trick, i.e., they learn a linear function in the space
induced by the respective kernel which corresponds to a non-linear function in
the original space. They differ in the loss functions (ridge versus
epsilon-insensitive loss). In contrast to SVR, fitting a KRR can be done in
closed-form and is typically faster for medium-sized datasets. On the other
hand, the learned model is non-sparse and thus slower than SVR at
prediction-time.</p>
<p>This example illustrates both methods on an artificial dataset, which
consists of a sinusoidal target function and strong noise added to every fifth
datapoint. The first figure compares the learned model of KRR and SVR when both
complexity/regularization and bandwidth of the RBF kernel are optimized using
grid-search. The learned functions are very similar; however, fitting KRR is
approx. seven times faster than fitting SVR (both with grid-search). However,
prediction of 100000 target values is more than tree times faster with SVR
since it has learned a sparse model using only approx. 1/3 of the 100 training
datapoints as support vectors.</p>
<p>The next figure compares the time for fitting and prediction of KRR and SVR for
different sizes of the training set. Fitting KRR is faster than SVR for medium-
sized training sets (less than 1000 samples); however, for larger training sets
SVR scales better. With regard to prediction time, SVR is faster than
KRR for all sizes of the training set because of the learned sparse
solution. Note that the degree of sparsity and thus the prediction time depends
on the parameters epsilon and C of the SVR.</p>
<ul class="sphx-glr-horizontal">
<li><img alt="../_images/sphx_glr_plot_kernel_ridge_regression_001.png" class="sphx-glr-multi-img first" src="../_images/sphx_glr_plot_kernel_ridge_regression_001.png" />
</li>
<li><img alt="../_images/sphx_glr_plot_kernel_ridge_regression_002.png" class="sphx-glr-multi-img first" src="../_images/sphx_glr_plot_kernel_ridge_regression_002.png" />
</li>
<li><img alt="../_images/sphx_glr_plot_kernel_ridge_regression_003.png" class="sphx-glr-multi-img first" src="../_images/sphx_glr_plot_kernel_ridge_regression_003.png" />
</li>
</ul>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none"><div class="highlight"><pre><span></span>SVR complexity and bandwidth selected and model fitted in 0.452 s
KRR complexity and bandwidth selected and model fitted in 0.173 s
Support vector ratio: 0.320
SVR prediction for 100000 inputs in 0.062 s
KRR prediction for 100000 inputs in 0.108 s
</pre></div>
</div>
<div class="line-block">
<div class="line"><br /></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="c1"># Authors: Jan Hendrik Metzen <[email protected]></span>
<span class="c1"># License: BSD 3 clause</span>
<span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">division</span>
<span class="kn">import</span> <span class="nn">time</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="k">import</span> <a href="../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="View documentation for sklearn.svm.SVR"><span class="n">SVR</span></a>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="k">import</span> <a href="../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="View documentation for sklearn.model_selection.GridSearchCV"><span class="n">GridSearchCV</span></a>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="k">import</span> <a href="../modules/generated/sklearn.model_selection.learning_curve.html#sklearn.model_selection.learning_curve" title="View documentation for sklearn.model_selection.learning_curve"><span class="n">learning_curve</span></a>
<span class="kn">from</span> <span class="nn">sklearn.kernel_ridge</span> <span class="k">import</span> <a href="../modules/generated/sklearn.kernel_ridge.KernelRidge.html#sklearn.kernel_ridge.KernelRidge" title="View documentation for sklearn.kernel_ridge.KernelRidge"><span class="n">KernelRidge</span></a>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Generate sample data</span>
<span class="n">X</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10000</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sin" title="View documentation for numpy.sin"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
<span class="c1"># Add noise to targets</span>
<span class="n">y</span><span class="p">[::</span><span class="mi">5</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">3</span> <span class="o">*</span> <span class="p">(</span><span class="mf">0.5</span> <span class="o">-</span> <span class="n">rng</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">//</span> <span class="mi">5</span><span class="p">))</span>
<span class="n">X_plot</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">100000</span><span class="p">)[:,</span> <span class="kc">None</span><span class="p">]</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Fit regression model</span>
<span class="n">train_size</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">svr</span> <span class="o">=</span> <a href="../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="View documentation for sklearn.model_selection.GridSearchCV"><span class="n">GridSearchCV</span></a><span class="p">(</span><a href="../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="View documentation for sklearn.svm.SVR"><span class="n">SVR</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'rbf'</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">),</span> <span class="n">cv</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span>
<span class="n">param_grid</span><span class="o">=</span><span class="p">{</span><span class="s2">"C"</span><span class="p">:</span> <span class="p">[</span><span class="mf">1e0</span><span class="p">,</span> <span class="mf">1e1</span><span class="p">,</span> <span class="mf">1e2</span><span class="p">,</span> <span class="mf">1e3</span><span class="p">],</span>
<span class="s2">"gamma"</span><span class="p">:</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.logspace.html#numpy.logspace" title="View documentation for numpy.logspace"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">)})</span>
<span class="n">kr</span> <span class="o">=</span> <a href="../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="View documentation for sklearn.model_selection.GridSearchCV"><span class="n">GridSearchCV</span></a><span class="p">(</span><a href="../modules/generated/sklearn.kernel_ridge.KernelRidge.html#sklearn.kernel_ridge.KernelRidge" title="View documentation for sklearn.kernel_ridge.KernelRidge"><span class="n">KernelRidge</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'rbf'</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">),</span> <span class="n">cv</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span>
<span class="n">param_grid</span><span class="o">=</span><span class="p">{</span><span class="s2">"alpha"</span><span class="p">:</span> <span class="p">[</span><span class="mf">1e0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">1e-2</span><span class="p">,</span> <span class="mf">1e-3</span><span class="p">],</span>
<span class="s2">"gamma"</span><span class="p">:</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.logspace.html#numpy.logspace" title="View documentation for numpy.logspace"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">)})</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">svr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="n">train_size</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="n">train_size</span><span class="p">])</span>
<span class="n">svr_fit</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"SVR complexity and bandwidth selected and model fitted in </span><span class="si">%.3f</span><span class="s2"> s"</span>
<span class="o">%</span> <span class="n">svr_fit</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">kr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="n">train_size</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="n">train_size</span><span class="p">])</span>
<span class="n">kr_fit</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"KRR complexity and bandwidth selected and model fitted in </span><span class="si">%.3f</span><span class="s2"> s"</span>
<span class="o">%</span> <span class="n">kr_fit</span><span class="p">)</span>
<span class="n">sv_ratio</span> <span class="o">=</span> <span class="n">svr</span><span class="o">.</span><span class="n">best_estimator_</span><span class="o">.</span><span class="n">support_</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">train_size</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Support vector ratio: </span><span class="si">%.3f</span><span class="s2">"</span> <span class="o">%</span> <span class="n">sv_ratio</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">y_svr</span> <span class="o">=</span> <span class="n">svr</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_plot</span><span class="p">)</span>
<span class="n">svr_predict</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"SVR prediction for </span><span class="si">%d</span><span class="s2"> inputs in </span><span class="si">%.3f</span><span class="s2"> s"</span>
<span class="o">%</span> <span class="p">(</span><span class="n">X_plot</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">svr_predict</span><span class="p">))</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">y_kr</span> <span class="o">=</span> <span class="n">kr</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_plot</span><span class="p">)</span>
<span class="n">kr_predict</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"KRR prediction for </span><span class="si">%d</span><span class="s2"> inputs in </span><span class="si">%.3f</span><span class="s2"> s"</span>
<span class="o">%</span> <span class="p">(</span><span class="n">X_plot</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">kr_predict</span><span class="p">))</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Look at the results</span>
<span class="n">sv_ind</span> <span class="o">=</span> <span class="n">svr</span><span class="o">.</span><span class="n">best_estimator_</span><span class="o">.</span><span class="n">support_</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">sv_ind</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">sv_ind</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s1">'r'</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'SVR support vectors'</span><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'data'</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">edgecolors</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">X_plot</span><span class="p">,</span> <span class="n">y_svr</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'r'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'SVR (fit: </span><span class="si">%.3f</span><span class="s1">s, predict: </span><span class="si">%.3f</span><span class="s1">s)'</span> <span class="o">%</span> <span class="p">(</span><span class="n">svr_fit</span><span class="p">,</span> <span class="n">svr_predict</span><span class="p">))</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">X_plot</span><span class="p">,</span> <span class="n">y_kr</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'g'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'KRR (fit: </span><span class="si">%.3f</span><span class="s1">s, predict: </span><span class="si">%.3f</span><span class="s1">s)'</span> <span class="o">%</span> <span class="p">(</span><span class="n">kr_fit</span><span class="p">,</span> <span class="n">kr_predict</span><span class="p">))</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s1">'data'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s1">'target'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'SVR versus Kernel Ridge'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">()</span>
<span class="c1"># Visualize training and prediction time</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="View documentation for matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
<span class="c1"># Generate sample data</span>
<span class="n">X</span> <span class="o">=</span> <span class="mi">5</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10000</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sin" title="View documentation for numpy.sin"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
<span class="n">y</span><span class="p">[::</span><span class="mi">5</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">3</span> <span class="o">*</span> <span class="p">(</span><span class="mf">0.5</span> <span class="o">-</span> <span class="n">rng</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">//</span> <span class="mi">5</span><span class="p">))</span>
<span class="n">sizes</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.logspace.html#numpy.logspace" title="View documentation for numpy.logspace"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int</span><span class="p">)</span>
<span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">estimator</span> <span class="ow">in</span> <span class="p">{</span><span class="s2">"KRR"</span><span class="p">:</span> <a href="../modules/generated/sklearn.kernel_ridge.KernelRidge.html#sklearn.kernel_ridge.KernelRidge" title="View documentation for sklearn.kernel_ridge.KernelRidge"><span class="n">KernelRidge</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'rbf'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
<span class="n">gamma</span><span class="o">=</span><span class="mi">10</span><span class="p">),</span>
<span class="s2">"SVR"</span><span class="p">:</span> <a href="../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="View documentation for sklearn.svm.SVR"><span class="n">SVR</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'rbf'</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mf">1e1</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mi">10</span><span class="p">)}</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">train_time</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">test_time</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">train_test_size</span> <span class="ow">in</span> <span class="n">sizes</span><span class="p">:</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="n">train_test_size</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="n">train_test_size</span><span class="p">])</span>
<span class="n">train_time</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">estimator</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_plot</span><span class="p">[:</span><span class="mi">1000</span><span class="p">])</span>
<span class="n">test_time</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">sizes</span><span class="p">,</span> <span class="n">train_time</span><span class="p">,</span> <span class="s1">'o-'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"r"</span> <span class="k">if</span> <span class="n">name</span> <span class="o">==</span> <span class="s2">"SVR"</span> <span class="k">else</span> <span class="s2">"g"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"</span><span class="si">%s</span><span class="s2"> (train)"</span> <span class="o">%</span> <span class="n">name</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">sizes</span><span class="p">,</span> <span class="n">test_time</span><span class="p">,</span> <span class="s1">'o--'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"r"</span> <span class="k">if</span> <span class="n">name</span> <span class="o">==</span> <span class="s2">"SVR"</span> <span class="k">else</span> <span class="s2">"g"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"</span><span class="si">%s</span><span class="s2"> (test)"</span> <span class="o">%</span> <span class="n">name</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xscale.html#matplotlib.pyplot.xscale" title="View documentation for matplotlib.pyplot.xscale"><span class="n">plt</span><span class="o">.</span><span class="n">xscale</span></a><span class="p">(</span><span class="s2">"log"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.yscale.html#matplotlib.pyplot.yscale" title="View documentation for matplotlib.pyplot.yscale"><span class="n">plt</span><span class="o">.</span><span class="n">yscale</span></a><span class="p">(</span><span class="s2">"log"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s2">"Train size"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"Time (seconds)"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Execution Time'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">"best"</span><span class="p">)</span>
<span class="c1"># Visualize learning curves</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="View documentation for matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
<span class="n">svr</span> <span class="o">=</span> <a href="../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="View documentation for sklearn.svm.SVR"><span class="n">SVR</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'rbf'</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mf">1e1</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="n">kr</span> <span class="o">=</span> <a href="../modules/generated/sklearn.kernel_ridge.KernelRidge.html#sklearn.kernel_ridge.KernelRidge" title="View documentation for sklearn.kernel_ridge.KernelRidge"><span class="n">KernelRidge</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'rbf'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="n">train_sizes</span><span class="p">,</span> <span class="n">train_scores_svr</span><span class="p">,</span> <span class="n">test_scores_svr</span> <span class="o">=</span> \
<a href="../modules/generated/sklearn.model_selection.learning_curve.html#sklearn.model_selection.learning_curve" title="View documentation for sklearn.model_selection.learning_curve"><span class="n">learning_curve</span></a><span class="p">(</span><span class="n">svr</span><span class="p">,</span> <span class="n">X</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span> <span class="n">train_sizes</span><span class="o">=</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span>
<span class="n">scoring</span><span class="o">=</span><span class="s2">"neg_mean_squared_error"</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="n">train_sizes_abs</span><span class="p">,</span> <span class="n">train_scores_kr</span><span class="p">,</span> <span class="n">test_scores_kr</span> <span class="o">=</span> \
<a href="../modules/generated/sklearn.model_selection.learning_curve.html#sklearn.model_selection.learning_curve" title="View documentation for sklearn.model_selection.learning_curve"><span class="n">learning_curve</span></a><span class="p">(</span><span class="n">kr</span><span class="p">,</span> <span class="n">X</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span> <span class="n">y</span><span class="p">[:</span><span class="mi">100</span><span class="p">],</span> <span class="n">train_sizes</span><span class="o">=</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mf">0.1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span>
<span class="n">scoring</span><span class="o">=</span><span class="s2">"neg_mean_squared_error"</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">train_sizes</span><span class="p">,</span> <span class="o">-</span><span class="n">test_scores_svr</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span> <span class="s1">'o-'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"SVR"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">train_sizes</span><span class="p">,</span> <span class="o">-</span><span class="n">test_scores_kr</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span> <span class="s1">'o-'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"g"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"KRR"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s2">"Train size"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"Mean Squared Error"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Learning curves'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">"best"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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